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    x: 1 5 9
    P(X=x): a b c

    where a,b,c are constants
    It is known that P(X<4)=P(X>4) and P(X <=5)=2P(X>5)

    How should i find a,b,c ?? can anyone help and show the work out ...thankyou

    You have 3 unknowns, so need to find 3 equations in terms of these unknowns.

    1) Use the fact that sum of all the probabilities = 1

    2) P(X<4)=P(X>4) - therefore 4 is the mean, so use the formula for the mean/expected value and set this equal to 4

    3) from P(X <=5)=2P(X>5),
    P ( 1 or 5) = 2 P(9)
    a+b = 2c

    There you have the 3 equations and then just solve them simultaneously.
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Updated: February 2, 2010

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